
Convergence: For FL convergence rate, there are still some key problems.
For example, there is a need for exact/more accurate convergence formulation with less assumptions and approximations [1]}, which should consistent with real FL experiment data.
Although there are some studies in this area, most of them related to convex loss function.
Besides, due to the heterogeneous property of quality of service, it is possible to simultaneously conduct multi-task FL.
In addition, for large-scale system, the multi-cell and multi-hop FL should be considered, which require one must have more insights on FL convergence analysis.
Moreover, one challenge is to study the mobility of wireless devices for FL convergence.
Due to the mobility, the channel gains between devices and BS are dynamically changed and it is possible that some devices will quit the FL process due to serious channel state information, which affects the convergence of the whole FL process.

Privacy and security: In terms of open problems for privacy and security, there is a need for the following study: privacy protection at each user, privacy protection at the BS, and security for the whole FL algorithm.
For privacy protection at each user and the BS, one of the key problem is to study the coding scheme and physical layer security technique.
For security of the whole FL algorithm, there is a need to study the encryption (such as quantum key distribution) and defender.

Performance evaluation:
One of the challenges is to investigate communication bandwidth for FL delay performance. FL on mobile phones relies on wireless communication to collaboratively learn a machine learning model. Although compute resources of mobile phones are becoming increasingly powerful, the bandwidth of wireless communication has not increased as much. As such, the bottleneck is shifted from computation to communication. As a consequence, limited communication bandwidth could incur long communication latency, and thus could significantly slow down the convergence time of the FL process.

FL for emerging technologies: The interplay between FL and emerging technologies introduces new challenges.
For instance, the very high propagation attenuations in THz can affect the convergence analysis.
For instance, in satellite communication, FL can used to optimize beam and location of the satellite.
For brain-computer, one of the challenge is to use FL extract deep knowledge of the brain's neural network.
In quantum communication, there is a need to use FL optimize the parameters (such as base probability) for quantum key distribution.

